How are the Marks of the Children of Kyorlin determined? I've noticed that sometimes I have units with 4+ Marks and other time I have units with only 1 Mark.

I believe when a child is born it has a 10% chance of getting each mark.
Also Epona increases your mark chances, i believe.

In my last game both of my Children born had the warmth mark. At first I did not truly appreciate the import of the warmth mark. After a bit I realised, I can stick them on blizzard duty and safely put cities outside of the small enclave.

I could never seem to find the blizzard's center, so warmth was useless to me.

You can find it with a mouse-over.

In combination with globe view to see where they are in general.

I have tried mousing over the blizard areas and have not found the blizard's center. What do you look for to find it? I have also found warmth to be pretty useless.

the center looks like it's raining in it. Kinda of crystal like lines in it.

When you do the mouse-over, the terrain info (in the lower left of the screen) shows blizzard. That's where you need to be for warmth to work. I've found Warmth to be quite useful, but not as useful as a Mobility-promoted Mammoth rider carrying the Orb of Succellus along a road network ;).

I had the blizzard problem too. I think the important bit is that a blizzard is a cloud high in the air, you need to look a tile or two below the cloud to find the blizzard tile. It's easier to find if, as mentioned, you skip out to globe view so you can look straight down on the cloud.

Does anybody have the full list of marks?

Bat - Can cast Haste (+1 :move: to living units in the stack)
Dog - +50% XP in combat
Horse - +1 :move: +1 First Strike
Rabbit - Can cast Floating Eye (Scouting device)
Rat - +20% :strength:
Raven - Can cast Raise Skeleton (cannon fodder free unit)
Scorpion - Can cast Warmth (destroys Blizzards)

Thanks. I did't see the conceptt first. I got three children with all rabbits, and thought that was a standard thing. Did't see why my nr 3 was weaker, without having a secondary mark. Must say that "Bat" mark was very useful :)
I used a skeleton for occuping the Doviellos copper mine for most of the game, but that feels like exploiting a bug, since they didn't attack it.

Thanks. I did't see the conceptt first. I got three children with all rabbits, and thought that was a standard thing. Did't see why my nr 3 was weaker, without having a secondary mark. Must say that "Bat" mark was very useful :)
I used a skeleton for occuping the Doviellos copper mine for most of the game, but that feels like exploiting a bug, since they didn't attack it.
The Doviello AI behavior is very odd. I can run my assassins around attacking(and capturing) their workers. They won't try to capture them. If I run a unit(such as a hunter escorting animals) through their territory, and surround them with captured workers, they will go around the workers to attack my hunter. Another unit they won't attack is captured Giant Spiders, though they will attack captured Mammoths and Wolfs.